Numerical approximation of linear parabolic evolution equations revisited

TL;DR

This paper derives convergence rates for numerical methods solving abstract linear parabolic equations in Banach spaces, extending existing results to more general equations and approximation techniques, including surface finite element methods.

Contribution

It provides generalized convergence estimates for a broad class of linear parabolic equations and numerical schemes, including surface finite element approximations.

Findings

Convergence rates are established for various numerical methods.

Results extend to parabolic equations on surfaces.

Applicable to finite element and surface finite element methods.

Abstract

We obtain rates of convergence of numerical approximations of abstract linear parabolic evolution equations in Banach spaces. Our estimates extend known results from the literature of finite element approximations of parabolic equations to more general equations and numerical approximation methods. As an example, we consider parabolic equations on surfaces and surface finite element approximations.